Detection of deep low-frequency earthquakes in the Nankai subduction zone over 11 years using a matched filter technique

To improve our understanding of the long-term behavior of low-frequency earthquakes (LFEs) along the tremor belt of the Nankai subduction zone, we applied a matched filter technique to continuous seismic data recorded by a dense and highly sensitive seismic network over an 11-year window, April 2004 to August 2015. We detected a total of ~ 510,000 LFEs, or ~ 23 × the number of LFEs in the JMA catalog for the same period. During long-term slow slip events (SSEs) in the Bungo Channel, a series of migrating LFE bursts intermittently occurred along the fault-strike direction, with slow hypocenter propagation. Elastic energy released by long-term SSEs appears to control the extent of LFE activity. We identify slowly migrating fronts of LFEs during major episodic tremor and slip (ETS) events, which extend over distances of up to 100 km and follow diffusion-like patterns of spatial evolution with a diffusion coefficient of ~ 104 m2/s. This migration pattern closely matches the spatio-temporal evolution of tectonic tremors reported by previous studies. At shorter distances, up to 15 km, we discovered rapid diffusion-like migration of LFEs with a coefficient of ~ 105 m2/s. We also recognize that rapid migration of LFEs occurred intermittently in many streaks during major ETS episodes. These observations suggest that slow slip transients contain a multitude of smaller, temporally clustered fault slip events whose evolution is controlled by a diffusional process.


Introduction
In the past two decades, slow earthquakes have been detected in many active plate boundaries along the Pacific Rim (Peng and Gomberg 2010;Obara and Kato 2016). Slow earthquakes occur primarily in partially coupled areas, such as the shallower and deeper extensions of the strongly locked seismogenic zone along a plate boundary fault (Obara and Kato 2016;Araki et al. 2017;Bartlow 2020;Wallace2020;Yokota and Ishikawa 2020).
In the Nankai subduction zone, slow earthquakes are typically classified as either seismic or geodetic events, based on their characteristic time scales (Obara and Kato 2016). Deep tectonic tremor, one type of slow seismic earthquake, is distributed quasi-continuously within a narrow belt-like zone along the downdip edge of the strongly locked seismogenic zone over a total length of ~ 600 km (Obara 2002;Obara and Kato 2016). The waveforms of this deep tremor contain relatively energetic and impulsive signals that have been identified as low-frequency earthquakes (LFEs) by the Japan Meteorological Agency (JMA) (Katsumata and Kamaya 2003;Shelly et al. 2007a). Previous studies have proposed that tectonic tremor can be explained by a swarm of LFEs, each of which occurs as shear slip along the plate boundary fault (Shelly et al. 2007a;Ide et al. 2007). Shelly et al. (2007b) applied a matched filter technique (MFT) to 2-week-long continuous seismograms from western Shikoku Island and found rapid hypocentral migration of deep LFEs at speeds of 25-150 km/h, especially in the along-dip direction, much faster than the along-strike migration rates Open Access *Correspondence: akato@eri.u-tokyo.ac.jp Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan of ~ 10 km/days associated with episodic tremor and slip (ETS) events. Owing to the limited analysis window, the long-term behavior of LFEs has not been well constrained. The JMA routinely determines hypocenters of LFEs to monitor temporal changes in the locking state along the Nankai subduction zone, but many LFEs in the existing catalog are missing because of overlapping waveforms during intensive burst-like LFEs and low signal-tonoise ratios (SNRs) of individual LFEs.
To improve our understanding of the behavior of longterm LFE activity along the tremor belt in Nankai, we applied the MFT to 11 years of continuous seismic data recorded by a dense, highly sensitive network, using LFEs with relatively high SNR values as template events. We examined the spatio-temporal evolution of LFEs and focused on interesting activity during two ETS episodes. We also identified numerous episodes of slow and rapid migration of LFEs during slow slip events (SSEs) along the Nankai subduction zone, indicating that a slow slip transient comprises many episodes of intermittent fault slip (Shelly et al. 2007b;Frank et al. 2018). The present study reports, for the first time, that rapid migration of LFEs appears to follow a diffusion law on shorter length scales. These features suggest that a diffusional process controls slow slip on multiple temporal and length scales.

Methods
We applied the MFT (Shelly et al. 2007a;Kato et al. 2013) to continuous waveform data retrieved by the Japanese national high-sensitivity seismograph network, Hi-net (NIED 2019a), and F-net (NIED 2019b), using three-component velocity seismograms from 1 April 2004 through 31 August 2015 (Fig. 1). As template events, we selected 3500 LFEs in southwestern Japan (western Shikoku and Tokai regions) from the JMA catalog (Additional file 1), recorded between 1 April 2004 and 31 August 2015 (Fig. 1). These selected LFEs have high signal-to-noise ratios (SNR). We divided the LFE zone into nine overlapping subregions (the MFT was executed for a total of 4147 events, because 647 templates are placed in the overlapping subregions), as shown in Fig. 1, and used selected template LFEs and  stations within each subregion for detection; we required ≥ 27 available channels on each local seismic network for a detected event to be retained. The continuous and template waveforms were preprocessed by applying a 2-6 Hz Butterworth bandpass filter and decimating the sampling rate from 100 to 20 Hz. We then extracted a 6.0-s data window, starting 3.0 s prior to the arrival of the synthetic S-wave, with synthetic arrivals calculated using the one-dimensional velocity structure used by the JMA for routine earthquake locations. The event detection threshold was set at 9× MAD, the median absolute deviation of the average correlation coefficient (ACC) calculated over each day. This level was chosen based on visual inspection of detected events, to suppress false detections while retaining as many true detections as possible. We assigned the location of the template event to each corresponding detection. We calculated the magnitude of the detected event based on the median value of the maximum amplitude ratios for all channels between the template and detected events, assuming that a tenfold increase in amplitude corresponds to a one-unit increase in magnitude (Peng and Zhao 2009).
To remove multiple detections, we used the template event location with the highest mean correlation coefficient in ± 6.0-s window from each detection. We also took away false detections corresponding to regular earthquakes in and around the studied region, based on the JMA hypocenter catalog. In addition, we removed false detections resulting from both temporal increases in the noise levels at local seismic stations and incident waveforms from distant moderate to large earthquakes [i.e., low cross-correlation coefficients with large amplitudes (ACC/MAD < 12 and magnitude ≥ 1.1)]. A total of 510,984 LFEs (Additional file 2) were detected along the Nankai subduction zone (Fig. 2), approximately 23 × the number in the JMA catalog for the same period.  Fig. 2); these correspond to geodetic detections of long-term slow slip events in the Bungo Channel using GNSS data (Yoshioka et al. 2015;Ozawa 2017). It is notable that series of LFE swarms occurred along strike intermittently during the long-term SSEs. These results are similar to bursts of LFEs detected during the 2006 SSE in the Mexican subduction zone (Frank et al. 2018). These observations suggest that a large-scale, longterm SSE contains a multitude of smaller, temporally clustered events (Jolivet and Frank 2020).
The equivalent moment magnitude of the 2010 SSE (Mw 6.9) in the Bungo Channel is larger than that of the 2014 event (Mw 6.5; Yoshioka et al. 2015;Ozawa 2017). The number of LFEs detected during the 2010 long-term SSE was also greater than the number detected during the 2014 event, indicating that the energy released by each SSE controls the extent of LFE activity. We also recognize a slight increase in the number of LFEs in 2006, which roughly corresponds to a minor long-term SSE (Mw ~ 6.3) reported by Takagi et al. (2019). This slight increase implies the occurrence of a smaller SSE than those in 2010 and 2014.
The 2011 Mw 9.0 Tohoku-Oki earthquake occurred during the analysis window. However, we observed no significant behavioral differences between LFEs before and after the megathrust rupture, except for an enhancement of rupture connectivity between several segments from Bungo Channel to the eastern Shikoku (red shaded bars in Fig. 2). The occurrence rate remained similar, regardless of stress perturbations induced by the megathrust rupture. This observation is consistent with Kono et al. (2020), who demonstrated that there were no temporal variations in the estimated rate of seismic moment release by tectonic tremor along the Nankai subduction zone as a result of the Tohoku-Oki earthquake. But, note that the spatiotemporal evolution of LFEs has changed from ~ 2012, in Shikoku island where major ETS episodes more frequently migrated long-distance through multiple segments than before the Tohoku-Oki earthquake. This behavioral difference has indicated an enhancement of rupture connectivity (Takagi et al. 2016), and resulted in an increase in the number of short-term SSEs with larger slip extent and seismic moment after 2012 (Hirose and Kimura 2020).
As a distinct example of an ETS episode (Fig. 3), major LFE activity was initiated beneath western Shikoku on 25 May 2012, then migrated eastward along strike, spreading over a distance of up to 100 km during the following 8 days. Five days later, a second burst of activity began further east, across an LFE gap. The secondary activity appears roughly in agreement with the extrapolated propagation of the front of the initial sequence. These migration fronts of LFEs showed clear parabolic curves (broken red lines in Fig. 3a); that is, the front location is proportional to the square root of time elapsed from the initial event ( ∼ √ Dt ). The diffusion coefficient D of the two sequences is ~ 10 4 m 2 /s, within the range of values reported by previous studies using tectonic tremor signals (Ide 2010;Ando et al. 2012).
Before the main front of the migrating LFEs was reached, minor LFE activity started at a position of − 210 km projected along strike, indicated by the gray dotted-line rectangle in Fig. 3a. The occurrence rate of minor LFEs rapidly increased, to ~ 8 × the base rate (8R in Fig. 3b), when the migrating front of the major LFEs merged with that of the minor ones. This observation suggests that a minor SSE combined with the major SSE propagating in the fault-strike direction. The merging of two SSEs probably caused local acceleration of fault slip, resulting in intensive LFE activity after the passage of the slip front. A temporal acceleration in slip induced by the merging of two SSEs has been reported along the Cascadia subduction zone based on geodetic measurements (Bletery and Nocquet 2020), but on a much larger scale.
As another example, Fig. 4a shows bilateral diffusion-like along-strike migration of the LFE front, with D = 10 4 m 2 /s, that initiated on 14 October 2009 in the eastern Kii Peninsula, Japan. Activation of LFEs started at a distance of ~ 55 km along strike with a delay of approximately 5 days relative to passage of the main SSE front, which was moving toward the southwest. Delayed LFEs occurred to fill the LFE gap. As observed in Cascadia (Wech and Bartlow 2014), weak tremor-less slip might occur within this gap when the main front undergoes early migration toward the southwest, resulting in the connection of two spatially disjoint LFE areas. The LFEs terminate at a reduced slip rate when the migrating slip front reaches a non-critically stressed patch (Wech and Bartlow 2014), but the slight increase in loading rate can trigger additional slip at a distance.
During the slow long-distance migrations of LFEs, the migration patterns are categorized as diffusion-like and linear-like styles. The diffusive migrations can be identified during the other periods as listed up in Additional file 3: Table S1, in addition to the two periods in Figs. 3 and 4. The diffusive migrations are often observed in the western Shikoku and the eastern Kii Peninsula. This may be due to a higher spatial resolution of LFEs at the two areas, where the radiated energies of tremors show the largest values among the entire tremor belt (Annoura et al. 2016), resulting in a high signal-to-noise ratio.
As shown in Figs. 3c and 4b, LFE activity occurred intermittently during or after the passage of the main . The vertical dashed line coincides with the timing at which the migrating front of LFEs passes. "R" indicates the LFE occurrence rate before the migration front passes. c A zoomed-in view of the gray dotted-line box in a front of migrating LFEs, indicated by striped patterns of intense activity that occurred as the front passed. Along the stripes, LFEs migrated in the along-dip and alongstrike directions. Intermittent LFEs were reported by Shelly et al. (2007b) for a few ETS episodes in western Shikoku. The present study discovers that intermittent LFEs are pervasive along the Nankai subduction zone and have occurred over at least the 11-year study window (Fig. 1). ETS also contains a series of smaller, temporally clustered slow slip transients, as seen during the long-term SSE at Bungo Channel (Fig. 2). These observations, on different temporal and spatial scales, imply that intermittent slow slip may be a scale-invariant property of slow earthquakes.
The intermittent stripes of activity show distinct spatial and temporal patterns in LFE swarm evolution over distances up to 15 km (Fig. 5). The migration speeds are quite fast, and reach ~ 60 km/h; similarly, the rapid LFE migrations of Shelly et al. (2007b) occurred at rates of 25-150 km/h in western Shikoku. Some of fast migrations in the western Shikoku obey a diffusion-like evolution (broken red lines in Fig. 5), while others can be explained by linear propagations. It is hard to convincingly demonstrate the diffusion-like migration at small scale, because the spatial scale is approaching the spatial resolution of LFE location and the number of events during each fast sequence becomes small. However, we believe that fast short-distance migration also follows a diffusional behavior as like the slow long-distance migration of ETS episodes (Figs. 3 and 4).
In the case of the diffusive migration, D is estimated to be ~ 10 5 m 2 /s, an order of magnitude greater than for slow long-distance migration of ETS episodes (Figs. 3 and  4). Rapid migration can have a short duration (~ 10 min) and small length scale (~ 15 km), in contrast to slow long-distance migration of ETS episodes (Figs. 3a and 4a). Along the Cascadia subduction zone, similar rapid migration of tremor streaks was reported by Ghosh et al. (2010). Most of the streaks propagated at velocities of 30-110 km/h, with a peak of ~ 70 km/h, over distances of < 40 km. Although Cascadia tremor migration speeds have the same velocity range as those in Nankai, the length scale in Cascadia is much greater than in Shikoku, which roughly corresponds to the width of the deep tremor band (Ide 2012).
In summary, slow long-distance migration of LFEs during an ETS episode contains a series of slip events comprising pulses of more rapid slip with short-distance migrations (Shelly et al. 2007b). The migration speed of LFEs increases with decreasing length scale, which is similar to observations of tectonic tremor migration (Houston et al. 2011;Obara et al. 2012). The present study suggests that high-speed migration of LFEs may follow a diffusion pattern, even at shorter length scales (Fig. 5). Two fast short-distance migrations in Fig. 5f, g occurred during the slow long-distance migration of ETS episodes shown in Fig. 3. These features imply that a diffusional process controls slow slip at multiple temporal and length scales. As Kano et al. (2018a) proposed, slow slip can be explained by a stress diffusion model with lubrication by fluid, consisting of along-strike heterogeneities in the effective strengths of brittle patches embedded in a ductile shear zone along the plate boundary fault.
We consider that the present LFE catalog (Additional file 2) will be useful for understanding the long-term behavior of minor and major slow slip events along the Nankai subduction zone. The present study uses only LFEs with relatively high SNR as template events to reduce the total computation time. The selected LFEs are representative of the overall behavior of slow slip transients, but increasing the number of template events in Other symbols and meanings are the same as in Fig. 3. b A zoomed-in view of the boxed area in a future work will allow us to examine the spatio-temporal evolution of LFE activity at finer scales.

Conclusions
To examine long-term LFE activity along the deep tremor belt in the Nankai subduction zone, we applied the MFT to 11 years of continuous seismic data recorded by a dense and highly sensitive seismic network, using LFEs with high signal-to-noise ratios as template events. We detected a total of 510,984 LFEs, ~ 23 × the number in the JMA catalog for the same period. During long-term SSEs in the Bungo Channel, a series of intermittent, migrating LFE bursts occurred along the fault-strike direction, with slow hypocentral propagation speeds. Elastic energy released by longterm SSEs appears to control the extent of LFE activity. Over distances of up to 100 km, we clearly identified slow, long-distance migrating fronts of LFEs during major ETS episodes, which evolve as a diffusion process along the fault-strike direction with a coefficient of ~ 10 4 m 2 /s. This slow, diffusion-like migration closely matches the spatial and temporal evolution of tremor reported by previous studies. At shorter distance scales, to ~ 15 km, we discovered rapid diffusion-like migration of LFEs with a coefficient of ~ 10 5 m 2 /s. Rapid migration of LFEs occurred intermittently in streaks during a major ETS episode. These observations indicate that a slow slip transient contains a multitude of smaller, temporally clustered fault slip events, which evolve as if governed by a diffusional process.